Quantitative Finance And Risk Management: A Physicist's Approach

Part VI: The Macro-Micro Model (A Research Topic)

Chapter List

Chapter 47: The Macro-Micro Model Overview (Tech. Index 4/10)
Chapter 48: A Multivariate Yield-Curve Lognormal Model (Tech. Index 6/10)
Chapter 49: Strong Mean-Reverting Multifactor YC Model (Tech. Index 7/10)
Chapter 50: The Macro-Micro Yield-Curve Model (Tech. Index 5/10)
Chapter 51: Macro-Micro Model Further Developments (Tech. Index 6/10)
Chapter 52: A Function Toolkit (Tech. Index 6/10)

Explicit Time Scales Separating Dynamical Regions

The Macro-Micro model was developed in a systematic program in the late 1980's. The first goal was to model phenomenologically the real-world statistical behavior of yield curves using multifactor models. The idea of different dynamics in different regimes is implied by real-world data. The second goal was to be able to provide a framework to price contingent claims.

The Macro-Micro model explicitly includes time scales. Standard model assumptions of the movements of financial variables do not include time scales that separate different dynamical regions. On the other hand, the behavior of these variables in the real world clearly exhibits a variety of time scales. Interest rates, FX rates, stock prices etc. behave very differently at long time scales (e.g. months) relative to their behavior at short time scales (e.g. days). However, the absence of time scales in standard models makes the description of these different behaviors at different time scales difficult or perhaps impossible to understand.

It is true that mean reversion parameters with units 1/time can be used. We make extensive use of mean reversion, in fact very strong mean reversion. However, the yield-curve data coupled with the...

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